New ideas are constantly emerging in mathematical statistics for better procedures and better ways to formulate problems. Often these ideas begin in an abstract or amorphous form with the chance of immediate practicality being far removed. Development of these ideas and related methods into techniques which can be applied to medical problems and the subsequent testing of the new techniques in actual real world situations are the objectives of this research grant. The exposure to all new theoretical developments in mathematical statistics through a close association with the Department of Statistics and the availability of a wide variety of medical problems from the statistical support service provided for the School of Medicine put the Division of Biostatistics in an advantageous position for carrying out these objectives. Four areas of mathematical statistics which are undergoing substantial progress currently and which have the potential for usefulness in medical problems are (1) force randomization schemes, (2) robust methods, (3) techniques for censored and categorical data, and (4) measures of reliability. Developments, both actual and potential, in each of these areas are discussed in Section 3 of this grant application after the progress to date has been summarized in Section 2. The relevance and potential usefulness for medical research is indicated as well. In Section 4 some of the larger projects which the Division of Biostatistics is involved and which have data bases for testing some of the new methods are described. However, research will not necessarily be limited to the four cited areas and the listed projects.